Stochastic Integration with Jumps

Klaus Bichteler

doi:10.1017/CBO9780511549878

Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of càglàd integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical engineering and finance who need to use stochastic differential equations.

Review of the hardback:‘The material in the book is presented well: it is detailed, motivation is stressed throughout and the text is written with an enjoyable pinch of dry humour.’

Evelyn Buckwar Source: Zentralblatt MATH

Review of the hardback:'The highlights of the monograph are: Girsanov-Meyer theory on shifted martingales, which covers both the Wiener and Poisson setting; a Doob-Meyer decomposition statement providing really deep information that the objects that can go through the Daniell-like construction of the stochastic. This is an excellent and informative monograph for a general mathematical audience.'

Source: EMS

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Stochastic Integration with Jumps

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xiv

Chapter 1 - Introduction
pp 1-42

Chapter 2 - Integrators and Martingales
pp 43-86

Chapter 3 - Extension of the Integral
pp 87-186

Chapter 4 - Control of Integral and Integrator
pp 187-270

Chapter 5 - Stochastic Differential Equations
pp 271-362

Appendix A - Complements to Topology and Measure Theory
pp 363-469

Appendix B - Answers to Selected Problems
pp 470-476

References
pp 477-482

Index of Notations
pp 483-488

Index
pp 489-501

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Stochastic Integration with Jumps

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